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Note on Bicomplex Matrices

Year 2018, , 46 - 56, 31.10.2018
https://doi.org/10.36753/mathenot.476793

Abstract

In this paper, we consider bicomplex numbers and bicomplex matrices. Firstly, we give some properties
of bicomplex numbers.After that we investigate bicomplex matrices using properties of complex matrices.
Then we define the complex adjoint matrix of bicomplex matrices and we describe some of their
properties. Furthermore, we give the definition of q-determinant of bicomplex matrices.

References

  • [1] Y. Alagöz, K. H. Oral, and S. Yüce, "Split quaternion matrices", Miskolc Mathematical Notes vol.13(2012), No.2, p.223-232
  • [2] G.Baley Price, An ˙Introduction to multicomplex spaces and functions, 1991, Monographs and textbooks inpure and applied mathematics, v.140;Marcel Gekker, Inc., 402 pp
  • [3] F.O.Farid ,Qing-Wen Wang and F. Zhang, "On the eigenvalues of quaternion matrices", Linear and Multilinear Algebra vol.59, no.4, April 2011, 451-473
  • [4] H. Kaya, "Genelle¸stirilmi¸s Bikompleks sayılar" , Yüksek Lisans Tezi , Bilecik ¸Seyh Edebali Üniverstesi, Bilecik, 2014
  • [5] M.E.Luna-Elizarraras, M.Shapiro, D.C. Struppa, A.Vajiac, "Bicomplex Numbers and their elementary functions CUBO". A Mathematical Journal vol.14, No:02, (61-80). June, 2012
  • [6] M. Özdemir, M. Erdo˘gdu and H. ¸Sim¸sek, "On the Eigen values and Eigenvectors of a Lorentzion Rotation Matrix by using split queternions". Adv.Appl. Clifford Algebras 24(2014), 179-192
  • [7] D.Rochon, M.Shapiro, "On algebraic properties of bicomplex and hyperbolic numbers", an. Univ. Oredea Fasc. Mat. 11 (2004) 71-110
  • [8] T. Ünal, "Kuaterniyonlar ve Kuaterniyon Matrisleri" , Yüksek Lisans Tezi, Dumlupınar Üniversitesi, Haziran, 2011.
  • [9] F. Zhang ,"Quaternions and Matrices of Quaternions" Linear Algebra Appl., vol 251, pp.21-57, 1997
Year 2018, , 46 - 56, 31.10.2018
https://doi.org/10.36753/mathenot.476793

Abstract

References

  • [1] Y. Alagöz, K. H. Oral, and S. Yüce, "Split quaternion matrices", Miskolc Mathematical Notes vol.13(2012), No.2, p.223-232
  • [2] G.Baley Price, An ˙Introduction to multicomplex spaces and functions, 1991, Monographs and textbooks inpure and applied mathematics, v.140;Marcel Gekker, Inc., 402 pp
  • [3] F.O.Farid ,Qing-Wen Wang and F. Zhang, "On the eigenvalues of quaternion matrices", Linear and Multilinear Algebra vol.59, no.4, April 2011, 451-473
  • [4] H. Kaya, "Genelle¸stirilmi¸s Bikompleks sayılar" , Yüksek Lisans Tezi , Bilecik ¸Seyh Edebali Üniverstesi, Bilecik, 2014
  • [5] M.E.Luna-Elizarraras, M.Shapiro, D.C. Struppa, A.Vajiac, "Bicomplex Numbers and their elementary functions CUBO". A Mathematical Journal vol.14, No:02, (61-80). June, 2012
  • [6] M. Özdemir, M. Erdo˘gdu and H. ¸Sim¸sek, "On the Eigen values and Eigenvectors of a Lorentzion Rotation Matrix by using split queternions". Adv.Appl. Clifford Algebras 24(2014), 179-192
  • [7] D.Rochon, M.Shapiro, "On algebraic properties of bicomplex and hyperbolic numbers", an. Univ. Oredea Fasc. Mat. 11 (2004) 71-110
  • [8] T. Ünal, "Kuaterniyonlar ve Kuaterniyon Matrisleri" , Yüksek Lisans Tezi, Dumlupınar Üniversitesi, Haziran, 2011.
  • [9] F. Zhang ,"Quaternions and Matrices of Quaternions" Linear Algebra Appl., vol 251, pp.21-57, 1997
There are 9 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Canan Ölçek This is me 0000-0003-3079-3577

Semra Kaya Nurkan 0000-0001-6473-4458

Publication Date October 31, 2018
Submission Date November 14, 2017
Acceptance Date October 3, 2018
Published in Issue Year 2018

Cite

APA Ölçek, C., & Nurkan, S. K. (2018). Note on Bicomplex Matrices. Mathematical Sciences and Applications E-Notes, 6(2), 46-56. https://doi.org/10.36753/mathenot.476793
AMA Ölçek C, Nurkan SK. Note on Bicomplex Matrices. Math. Sci. Appl. E-Notes. October 2018;6(2):46-56. doi:10.36753/mathenot.476793
Chicago Ölçek, Canan, and Semra Kaya Nurkan. “Note on Bicomplex Matrices”. Mathematical Sciences and Applications E-Notes 6, no. 2 (October 2018): 46-56. https://doi.org/10.36753/mathenot.476793.
EndNote Ölçek C, Nurkan SK (October 1, 2018) Note on Bicomplex Matrices. Mathematical Sciences and Applications E-Notes 6 2 46–56.
IEEE C. Ölçek and S. K. Nurkan, “Note on Bicomplex Matrices”, Math. Sci. Appl. E-Notes, vol. 6, no. 2, pp. 46–56, 2018, doi: 10.36753/mathenot.476793.
ISNAD Ölçek, Canan - Nurkan, Semra Kaya. “Note on Bicomplex Matrices”. Mathematical Sciences and Applications E-Notes 6/2 (October 2018), 46-56. https://doi.org/10.36753/mathenot.476793.
JAMA Ölçek C, Nurkan SK. Note on Bicomplex Matrices. Math. Sci. Appl. E-Notes. 2018;6:46–56.
MLA Ölçek, Canan and Semra Kaya Nurkan. “Note on Bicomplex Matrices”. Mathematical Sciences and Applications E-Notes, vol. 6, no. 2, 2018, pp. 46-56, doi:10.36753/mathenot.476793.
Vancouver Ölçek C, Nurkan SK. Note on Bicomplex Matrices. Math. Sci. Appl. E-Notes. 2018;6(2):46-5.

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